(4w+9)(6-w)=0

Solution for (4w+9)(6-w)=0 equation:

(4w+9)(6-w)=0

We add all the numbers together, and all the variables

(4w+9)(-1w+6)=0

We multiply parentheses ..

(-4w^2+24w-9w+54)=0

We get rid of parentheses

-4w^2+24w-9w+54=0

We add all the numbers together, and all the variables

-4w^2+15w+54=0

a = -4; b = 15; c = +54;
Δ = b2-4ac
Δ = 152-4·(-4)·54
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-33}{2*-4}=\frac{-48}{-8}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+33}{2*-4}=\frac{18}{-8}
=-2+1/4
$